Keep divided edge straight when dragging it's end point
You may not be able to move other than the active one the way you want by dragging, but you might get closer to what you want to achieve, by using, in addition to the grab tool—G, the rotate tool—R, and the scale tool—S. If I were wanting to do what you want, I'd select all three vertices, with the grab tool, and move the active vertex to where you want it to end up. Then I'd use the rotate tool to adjust the location of the end vertex furthest from the active vertex, so that it is located on a line from the the new location of the active vertex and the location at which you want the furthest vertex to line up. Then, I'd use the scale too to actually set the location of the furthest vertex. 

Note that in doing it this way, it is important to select the vertices in the correct order. First select the vertex furthest from the vertex you want to be the active vertex, then select any intermediate vertices, and finally select what you want to be the active vertex. 

Also, if precise placement of the intermediate vertices is desired, I sometimes find it useful to count the number of intermediate vertices, delete them, place the two endpoints, create the edge, and then subdivide the edge into the required number of vertices. If there is other geometry incorporating those intermediate vertices, sometimes I don't delete them, but rather merge them into the intermediate vertices of the edge I created and subdivided.